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Posterior distribution when $Y_{1}=-2.5$ and $Y_{2}=2.5$
\vspace*{1em}

\begin{tabular}{l|lll|lll|lll}\hline
 & \multicolumn{3}{|c|}{$n=100$} & \multicolumn{3}{|c|}{$n=500$} &  \multicolumn{3}{|c}{$n=\infty$}  \\ \cline{2-10}
 & \multicolumn{2}{c}{ideantified} & mean & \multicolumn{2}{c}{identified} & mean & \multicolumn{2}{c}{identified} & mean \\ 
 & \multicolumn{2}{c}{interval} & width & \multicolumn{2}{c}{interval} & width & \multicolumn{2}{c}{interval} & width\\ \hline 
& -2.50 &  2.50 &  5.00 & -2.50 &  2.50 &  5.00 & -2.50 &  2.50 &  5.00 \\ \hline 
 & mean & \multicolumn{2}{c|}{90\% CI} & mean & \multicolumn{2}{c}{90\% CI} & mean & \multicolumn{2}{c}{90\% CI} \\ \hline 
prior 1 &  0.00 & -2.25 &  2.25 &  0.00 & -2.25 &  2.25 &  0.00 & -2.25 &  2.25 \\ 
prior 2 &  0.00 & -1.59 &  1.59 &  0.00 & -1.59 &  1.59 &  0.00 & -1.59 &  1.59 \\ 
prior 3 & -2.45 & -2.66 & -2.33 & -2.45 & -2.57 & -2.42 & -2.45 & -2.50 & -2.50 \\ 
prior 4 &  2.45 &  2.33 &  2.66 &  2.45 &  2.42 &  2.57 &  2.45 &  2.50 &  2.50 \\ \hline 
\end{tabular}

\vspace*{2em}
Posterior distribution $Y_{1}=-0.05$ and $Y_{2}=0.05$
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\begin{tabular}{l|lll|lll|lll}\hline
 & \multicolumn{3}{|c|}{$n=100$} & \multicolumn{3}{|c|}{$n=500$} &  \multicolumn{3}{|c}{$n=\infty$}  \\ \cline{2-10}
 & \multicolumn{2}{c}{ideantified} & mean & \multicolumn{2}{c}{identified} & mean & \multicolumn{2}{c}{identified} & mean \\ 
 & \multicolumn{2}{c}{interval} & width & \multicolumn{2}{c}{interval} & width & \multicolumn{2}{c}{interval} & width\\ \hline 
& -0.08 &  0.08 &  0.16 & -0.05 &  0.05 &  0.11 & -0.05 &  0.05 &  0.10 \\ \hline 
 & mean & \multicolumn{2}{c|}{90\% CI} & mean & \multicolumn{2}{c}{90\% CI} & mean & \multicolumn{2}{c}{90\% CI} \\ \hline 
prior 1 &  0.00 & -0.15 &  0.15 &  0.00 & -0.08 &  0.08 &  0.00 & -0.05 &  0.05 \\ 
prior 2 &  0.00 & -0.15 &  0.15 &  0.00 & -0.08 &  0.08 &  0.00 & -0.04 &  0.04 \\ 
prior 3 & -0.08 & -0.23 &  0.07 & -0.05 & -0.12 &  0.02 & -0.05 & -0.05 & -0.05 \\ 
prior 4 &  0.08 & -0.07 &  0.23 &  0.05 & -0.02 &  0.12 &  0.05 &  0.05 &  0.05 \\ \hline 
\end{tabular}

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